Dan Brown(click on names to see more mathematical fiction
by the same author)

...

The last act of a dying curator at the Louvre is an attempt to pass on, in code, a secret that he did not want to take to the grave. Among the things needed to "decode" this secret message is a recognition of the Fibonacci sequence, its connection to the "golden ratio", and the connection of the golden ratio to the pentagram. Yet another connection mentioned in the book, as one might guess from the title, the supposed connection of the golden ratio to the shape of the head in Da Vinci's "Mona Lisa".

The only other mathematics in the book is frequent vague references to mathematics in cryptography and a puzzle which involves relatively nonmathematical knowledge of Isaac Newton.

In fact, although this book was stunningly popular and was turned into a film, I'm not really happy with the presentation of the "golden ratio". For one thing, he says that it is equal to 1.6180. In fact, this rather famous number is equal to half of the sum of 1 and the square root of 5. Perhaps its most simple definition is that it is the positive root of the polynomial p(x)=x^2-x-1. Being an irrational number, it cannot be written as a finite decimal expansion, so Brown is being mathematically imprecise when he claims that it is 1.6180=1618/1000. Moreover, he repeats many ridiculous claims about the significance of this number which grow out of a kabalistic desire to find favorite numbers in nature. (The claims that this ratio is to be found in the human body sound too good to be true, and I have not yet seen any convincing evidence that this is anything more than wishful thinking.) Though, it must be admitted that the number has some properties of natural interest (see Ivars Peterson's account of its significance to the distribution of seeds in a sunflower and this page that explains why Fibonacci numbers arise naturally when discussing gender ratios in bees) there is a tendency in the media to overstate the significance of this number. I think that someone who brags about being the son of a math professor (see Digital Fortress) could have done better.

My point, then, is this: Throughout the book Brown tries to "wow" the reader with apparently amazing true facts that he has pieced together into this novel that combines espionage, religion and conspiracy theory...but don't take these "facts" too seriously. He's not being very careful with them. Remember "it's just a story". Just as I criticize his math, it seems that experts in just about every other area similarly criticize Brown's handling of their topic. (For instance, art historians will tell you that nobody refers to Leonardo Da Vinci as "Da Vinci"...it's not his name it just tells where he's from. His name was Leonardo. Historians of the church will tell you that it is inaccurate to suggest that before Constantine, Jesus was not considered divine. And, even though I am not a Christian, I do think that the text of the Gospels and the letters of Paul were written before Constantine and confirm that at least some people presented Jesus as being divine. Opus Dei, which is a real organization, of course objects strongly to their portrayal in this book.) Now, you can consider all of this to just be part of "the conspiracy" if you want...

Contributed by
Anonymous

A wonderful book that I enjoyed reading! I'm now searching for his book "Digital Fortress" and reading "Angels and Demons". Good work, Dan Brown! About the math: he added the Fibonacci Code, and some other small tidbits. Logic was the main point in this amazing book.

If you haven't read the book yet, please stop reading this posting now. I'm going to say some things which could spoil your enjoyment of it. However, I'd like to discuss some things from the book that didn't make sense to me. If I'm right that these things don't make sense, then you can consider this "fair criticism" of the book. On the other hand, it may simply be that I'm failing to understand something, in which case I'd appreciate an explanation or correction from someone else.
Okay, here it goes:

So, there's this organization whose sole purpose is to preserve the memory of the fact that women are important and the story of one woman who was kept out of power unfairly. Fine. Doesn't it seem strange though that all of the leaders of this group are men?

It makes no sense at all to me why this group would continue to keep this secret. If they want people to know about it, they would tell people. If they want it to remain secret, why go through so much trouble to preserve it. The explanation at the end that they want people to include mention of this fact secretly in just about every famous work of art, fiction or film that you can name makes no sense either. Why do they want it presented just in the form of symbolism? How can it be a secret if it seems that just about everyone knows about it?

Why is the bloodline of Jesus so important if, as they maintain, he was just a person? Why risk the lives of so many people (the family themselves and the others who die to protect them)? The fact that Jesus supposedly had kids is an interesting fact in itself, but maintaining who their decendents are seems pointless if there is not supposed to be something mystical or magical about them. Moreover, if they believe the bible to be nothing but myths with weak basis in fact, exactly who are they praying to at the tomb of the "Grail"?

Anyway, I agree that it was a fun book to read...I just wish that it made more sense in the end.

Contributed by
d. Wallis

Cliche ridden prose sketches flimsy characters who perform as mouths for theories cobbled from many other authors. Twisting fiction with bits of fact results in a stupefyingly muddled plot. The most astounding thing about this book is that such marginally mediocre writing has become a cultural phenomenon.

Contributed by
Anonymous

You are all worthless. Just accept a work of fiction as fun.

Sure, I can do that with a Bugs Bunny cartoon. But, if a novel I am reading is so poorly crafted that I cannot believe the characters are real, if the author's ignorance of the subject is so apparent as to obscure the plot, if it seems like just a little bit of effort on the part of the author would have made it a good deal less stupid, then I don't really think it is very much fun to read. "Worthless" though my opinion may be, there it is.

Contributed by
Jeanne Lucas

I'm not a math person but from my further reading on cultural, historical, and theological ideas upon which the Da Vinci code is based, I wanted to respond to your three criticisms/questions.

The list of Grand Masters of the Priory of Sion (according to the documents "found" at the Louvre) did include some women. Women were supposedly involved in the organization up to the highest levels. Powerful and influential people tended to dominate the list and women simply weren't very powerful or influential for most of history - of course, the whole list is probably bogus but for what it's worth. you can find that list in "Holy Blood, Holy Grail."

the whole secret society thing. Yeah. Well, Christianity itself was something of a secret society in the beginning, keeping under wraps, communicating through symbols and code and we know that there are secret societies and have been probably throughout history - from freemasonry to college sororities. So for some reason humans seem to like the idea of having these secret societies and they all purport to have some important secret that they keep. It's kind of like Jefferson's idea of democracy. You can't give all the information and power to everybody, you have to be selective about when people are ready for it because if it fell into the wrong hands... who knows? And the idea of imbedding the idea of the sacred feminine into the cultural legacy of art, music, etc. I think it has more to do with reaching people's subconcious with the idea than leaving an encoded record.

As for the bloodline of Christ, I agree. If there is a bloodline, it's so diffused by now, who cares? The idea purported in "Holy Blood, Holy Grail"
is not so much that the bloodline is divine as that it is royal. Mary Magdalene being of the royal line of Benjamin and Jesus the royal Bloodline of David, their offspring would be heirs to the throne of Israel. But there's so many people fighting over Israel these days, who is going to care if somebody shows up with a blood claim to a kingship that hasn't existed for centuries. Anyway, just my two cents. I was glad to see the comments on the mathematical claims in the book. I had my doubts about the whole golden ratio thing. I have to say that even though a lot of people have debunked the specific claims that Dan Brown made, his compiling so many ideas from so many different disciplines to create this story and to write such an exciting work of fiction out of it, well, that's pretty impressive. And I know so many people who have been spurned to read up on things by reading the book and learned things they didn't know or thought about things they hadn't thought about before and to me, that's the best kind of book I know. Thanks!
Jeanne

Contributed by
Sam Walker

While I think it is important that what is pretty much a thinly-cloaked criticism of Christianity is so popular in America, I too was left with a bad taste in my mouth from all the bad facts in this book. In the part where the Last Supper painting is described, I actually looked at a copy of the Last supper to find that many of the "facts" about the depiction of Mary Magdeline and Jesus are simple not in the painting at all. Likewise with some of the other works of art he mentions. There is no anonymous hand holding a dagger in the Last supper, and Peter is not menacingly leaning forward to cut Mary's throat. Likewise, in Madonna On The Rocks the hand does not appear at all like a claw.

Contributed by
Anonymous

This comment is mostly an answer to the last comment posted, about content of the images "Madonna (Virgin) on the Rocks" and "Last Supper" mentioned in the book.
While it is matter of personal interpretation how thretening hands of Madonna, Uriel and Peter look in the three pictures involved, I do not think that anyone
can misunderstand angry "US Army Sargent like" Peter facial expression toward
the character in the painting supposed to be Mary Magdalene in the book.
"Unaccounted hand with the knife": it appears between Peter and the character directly in front of him (in front of Peter and behind the character,
to the viewers left,...). Physically it can't belong to any characters arround
but if painting have been done by someone other than DaVinci, one could assume unnaturally extended hand of supposed "Mary Magdalene" going between Peter and
the other character). Enough for literary license in my opinion for all the "facts".

Contributed by
Steve

Whatever the actual 'factual' worth of the material within 'The Da Vinci' code, it is apparanent nonetheless that it is a darn good read.
The beauty of the novel lies not within its maths or historical accuracy, but in its gripping race against time that the main characters face.
The whole novel is played out over a fairly short 2 day period and is evenly action packed with enough conspiracies that would keep most readers glued to the pages.
The proof of the pudding is in the eating and I think if the majority of the readers thought they were reading tripe, then it would have not gotten to and stayed at the number one spot for so long.
Recommended.

Contributed by
shelly

It was an excellent book and thrilling . I don know much about the math part of it but the way things are put by the author you feel that he is releaving facts and not fiction .Worth reading !!!!!!!!

(Note: I think "feel that" is an important phrase in the preceding comment. In other words, the "facts" you are "learning" should not to be taken too seriously.)

Contributed by
Anonymous

First of all, those people that took this book as anything but fiction should not be reading this type of material. Personally, I really enjoyed the story. It had some factual and mythological material woven into the plot quite well. For it's "factual inconsistancies", as some folks call them, I say SO WHAT. It's fiction. Sure, it would be really something if this was 100% historically accurate, and his premise was real, but it's not. I think it struck a nerve with so many people because there seems to be a spiritual upheaval in the world, with the scandals in the Catholic Church, and the money grubbing televangelists smeared across our conciousness almost daily. Some have taken this work a bit too seriously, however, and seem almost threatened by it ("How dare he question religion?!?!?"). The thing is - you don't need to look too hard to find the facts that were given the "artistic license" once-over, and Mr. Brown isn't preaching that this book is true either. I put this in the same catergory as some Tom Clancy novels: intriguing, a clever blend of facts and fiction, thought provoking, and overall a perfectly good read.

Contributed by
Blackrat

There seems to be a host of religious fanatics ganging up on this novel because of it's content. All I can say is - What a great read - and that's what it's all about, isn't it for goodness sake.
Forget the facts that are presented (which you will find ARE true if you only researched a little more) just enjoy the ride. It's always been the case that christian die hards (particularly the catholic church) tend to rubbish anything that is said against their fantasy dogma. WELL TAKE A BREAK.
Just enjoy.

Contributed by
Alex Kasman

I'm far from a religious fanatic. I like to think I'm not a fanatic of any kind, but some might argue that I'm am the opposite of a relgious fanatic, which would be a sort of fanatic in itself. However, I must say that I don't agree with the statement that the "facts" in this book which have upset Christians, especially Catholics, are true. Quite a bit of it, like in all of Brown's books, is just made up to be entertaining fiction to those who don't care whether or not it is true. However, the "facts" that he's utilizing here are a conspiracy theory which, like so many others, seems sensible and to have evidentiary support only until you look at it more deeply and realize it is nothing more than a scam.

Enjoy the book or don't, but do not fool yourself into thinking that you're learning "the truth".

Contributed by
Anonymous

If you liked Da Vinci Code (or ESPECIALLY if you hated it) check out the clever and entertaining homage/parody at DaVinciDagger.com!

Contributed by
Simon

The first article [stated]: “The claims that this ratio is to be found in the human body or in the ratio of male to female bees in bee colonies sound too good to be true, and are.”. This is a tad harsh and I believe, at least in the case of the bees example, incorrect. From http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/ (which has lots of interesting information on the Fibonacci series and golden section):

“Sex ratio and sex allocation in sweat bees (Hymenoptera: Halictidae) D Yanega, in Journal of Kansas Entomology Society, volume 69 Supplement, 1966, pages 98-115.
Because of the imbalance in the family tree of honeybees, the ratio of male honeybees to females is not 1-to-1. This was noticed by Doug Yanega of the Entomology Research Museum at the University of California. In the article above, he correctly deduced that the number of females to males in the honeybee community will be around the golden-ratio Phi = 1.618033.. .”

I don’t like the story too much but at least he tries to get some maths in there.

Aha, I see that I was a bit too skeptical when it came to phi and bees. My original objection was that the number phi is irrational, and so with a finite number of bees the ratio of female to male bees cannot be exactly equal to this value, and I had never heard anyone describe how this "fact" was determined or why it was supposed to be true. However, inspired by Simon's message above, I looked into it a little further and found out that it does make complete sense! It is a simple consequence of the mating patterns of bees.

You see, male bees only have one parent (since they are produced through parthenogenesis) while female bees have two parents (being produced by sexual reproduction). This means that a male bee has only one parent, but three grandparents, 5 great-grandparents, 8 great-great-grandparents, etc. It is this natural occurence of the Fibonacci numbers that accounts for the apparent occurence of the golden mean in this context.

I stand corrected and will change the earlier text accordingly.

Contributed by
Andrew

However much you like or dislike this book, it askes the readership to question history. As stated correctly the winner always gets to writes it. So it askes you to question the development of the Christian church. You are free to expolore the issues raised and free to fully or partly accept , or reject the presented evidence. What is central in this book is the historical and present role of women, whose role has often been suppressed by men who have power and contol, this power can gainned from religion or politics or by any other means.It now asks is this control over women acceptable? The simple answer is --NO.

Contributed by
Caroline

I have just finished reading The Da Vinci code after much hype about it (and a documentary) inspired me to buy a copy (adding to the already high sales of the book). I cannot stand being ignorant to what so many others are talking about ... constantly. Like the time-line of the book, it took me two days to read! I could not put it down. I have read the other comments on this web-site and can only say one thing ... I cannot believe some of the absurd comments people make! Half of you can't even spell! Let me put it this way ... it is a thought provoking novel. It ought to cause you to think about the very real possibility that history may have been manipulated by some, perhaps sexist, but definitely dictatorial people. Whether it is true, factual or purely fictional or has some really inaccurate mathematecal [sic] notions is irrelevant. This book has inspired me to read about the Life of Jesus Christ ... on the Internet! I don't even bother with the Internet at the best of times, now I am reading about Jesus Christ? I am not a practising Catholic but I have been raised a Catholic. I believe that I am generally just a good person. But I tell you what, reading about Jesus Christ and his ministry, etcetera, I realise how absurd it all really sounds. So forget about the intracacies of the story, and consider the potential for the past 2000 years or whatever it works out to be, Christianity as we know it may all be a fabrication, and the concepts set forth by Dan Brown may be suprisingly real.

Contributed by
Freethunk

Yeah, so the book might get you thinking about the possibility that religion is made up. If this book does that for you, that's cool with me. Still, I kinda thought the book was lame as fiction. If you want a chance to think about religion critically, there are lots of better places to get it than this cheesy novel. If you want to read old stuff, check out Thomas Paine's The Age of Reason. And the movie The God Who Wasn't There is the most recent. Plenty of other authors have written about these ideas in between without hamming it up Dan Brown-style.

Contributed by
D

To the Unknown fellow who commented on the phantom knife in Leonardo's "Last Supper": The knife belongs to the Peter; his wrist is simply turned inward with the knife facing out. You'd think authors would be a bit more attentive to their subject matter. But if a gross factual error made me a mint...

Contributed by
Martin

If you like maths and are interested in The Da Vinci Code, then you might want to take a look at The Da Vinci Game at http://www.thedavincigame.com.

It's a fun board game with 800 challenges, including 200 Logic Keys which have a numerical answer, some of these require maths, many of them require lateral thinking. There are also riddles, anagrams and geography challenges which players race against each other and the clock to solve.

Hope you like the game!

Contributed by
Bill

Sorry, my comment doesn't really detail math much but I did want to address a couple prior comments:

D:
The hand with the knife, as I see it in the image at http://www.eskimo.com/~rwb/images/europe/11-milan-last-supper.jpg does appear out of place. The sleeve of the mystery arm is red or a dark brown and doesn't really match the other clothing shown on the people in that side of the table so I'm not sure it can be so easilly attributed to Peter. Also, the angle of the hand looks physically impossible based on Peter's current position. This image (http://www.fotos.org/galeria/showphoto.php/photo/2199/size/big/sort/1/cat/522/page/1) seems to be cleaned up and does a pretty good job of showing the color alternation between Jesus's clothing and that of Mary.

Sam Walker:
The hand/dagger is there. Also, the hand near "Mary's" throat could easilly be interpreted as either a friendly or angry gesture (though to me it looks like Peter is whispering in her ear; easiest to see in this copy of the image: http://fits.depauw.edu/aharris/Courses/ArtH132/galleries/images/fullsize/fs_da_Vinci_Last_Supper_cleaned.jpg). The face of Peter doesn't look friendly.

In the "Madonna" images I think it is interesting just to look at the two different images side by side:
The more modern version : http://astro.berkeley.edu/~kalas/disksite/images/rocks.jpg
The original:
http://www.artchive.com/artchive/L/leonardo/leonardo_virgin.jpg.html

In the original the angels hand does point at John the Baptist (though the whole angle is kind of wierd looking) and Mary's right hand, compared to the newer image, is a bit "clawlike" - it definitly doesn't have the same gentle look to it as the more recent image. There is an interesting write up of the two images here: http://www.lairweb.org.nz/leonardo/rocks.html

Finally, to deal with math and the Golden Number/Ratio - This article does a pretty good job of discussing how/why the ratio appears so often in nature: http://mathforum.org/library/drmath/view/52676.html

Contributed by
John Brazier

I prefer it as a novel - I think (this comment is open to criticism) that apart from the few mathmatical references, it is entirely fiction and should be treated as such to be appreciated fully. However - despite your critiscims about his defining of the divine sequence, it was actually this book that got me interested in phi and now i am researching it, aiming to write a prize essay about it (i am 14)

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